Problem: Tiffany is 2 years older than Emily. Tiffany and Emily first met 3 years ago. Two years ago, Tiffany was 3 times as old as Emily. How old is Tiffany now?
Explanation: We can use the given information to write down two equations that describe the ages of Tiffany and Emily. Let Tiffany's current age be $t$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $t = e + 2$ Two years ago, Tiffany was $t - 2$ years old, and Emily was $e - 2$ years old. The information in the second sentence can be expressed in the following equation: $t - 2 = 3(e - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $t$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = t - 2$ . Substituting this into our second equation, we get the equation: $t - 2 = 3($ $(t - 2)$ $ -$ $ 2)$ which combines the information about $t$ from both of our original equations. Simplifying the right side of this equation, we get: $t - 2 = 3t - 12$ Solving for $t$ , we get: $2 t = 10$ $t = 5$.